# Local semiconvexity of Kantorovich potentials on non-compact manifolds

ESAIM: Control, Optimisation and Calculus of Variations (2011)

- Volume: 17, Issue: 3, page 648-653
- ISSN: 1292-8119

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topFigalli, Alessio, and Gigli, Nicola. "Local semiconvexity of Kantorovich potentials on non-compact manifolds." ESAIM: Control, Optimisation and Calculus of Variations 17.3 (2011): 648-653. <http://eudml.org/doc/272798>.

@article{Figalli2011,

abstract = {We prove that any Kantorovich potential for the cost function c = d2/2 on a Riemannian manifold (M, g) is locally semiconvex in the “region of interest”, without any compactness assumption on M, nor any assumption on its curvature. Such a region of interest is of full μ-measure as soon as the starting measure μ does not charge n – 1-dimensional rectifiable sets.},

author = {Figalli, Alessio, Gigli, Nicola},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Kantorovich potential; optimal transport; regularity},

language = {eng},

number = {3},

pages = {648-653},

publisher = {EDP-Sciences},

title = {Local semiconvexity of Kantorovich potentials on non-compact manifolds},

url = {http://eudml.org/doc/272798},

volume = {17},

year = {2011},

}

TY - JOUR

AU - Figalli, Alessio

AU - Gigli, Nicola

TI - Local semiconvexity of Kantorovich potentials on non-compact manifolds

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2011

PB - EDP-Sciences

VL - 17

IS - 3

SP - 648

EP - 653

AB - We prove that any Kantorovich potential for the cost function c = d2/2 on a Riemannian manifold (M, g) is locally semiconvex in the “region of interest”, without any compactness assumption on M, nor any assumption on its curvature. Such a region of interest is of full μ-measure as soon as the starting measure μ does not charge n – 1-dimensional rectifiable sets.

LA - eng

KW - Kantorovich potential; optimal transport; regularity

UR - http://eudml.org/doc/272798

ER -

## References

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